The document discusses transmission lines, focusing on the equations governing their behavior, including Kirchhoff's laws and the use of phasors for AC signals. It covers the derivation of wave equations, highlighting the attenuation and phase constants and the transition to uncoupled forms. Additionally, it mentions the characteristics of lossless and non-dispersive transmission lines.

1. INTRODUCTION TO
TRANSMISSION LINES
PART II
DR. FARID FARAHMAND
FALL 2012

2. Transmission Line Model

3. Perfect Conductor and Perfect Dielectric (notes)

4. Transmission-Line Equations
Kirchhoff Voltage Law:
Vin-Vout – VRʼ – VLʼ=0
Kirchhoff Current Law:
Iin – Iout – Icʼ – IGʼ=0
Note:
VL=L . di/dt
Ic=C . dv/dt
Remember:
2
2
|
|
;
tan
1
|
|
|
)
(
|
)
(
]
Im[
)
sin(
]
Re[
)
cos(
)
sin(
)
cos(
B
A
C
A
B
jB
A
C
e
e
z
E
z
E
Ae
A
Ae
A
Aj
A
Ae
j
j
j
j
j
z
+
=
=
→
+
=
=
=
=
=
+
=
θ
θ
θ
θ
θ
θ
θ
θ
θ
θ

5. Transmission-Line Equations
ac signals: use phasors
Transmission
Line Equation
in Phasor
Form

6. Derivation of Wave Equations
Combining the two equations leads to:
Second-order differential equation
complex propagation
constant
attenuation constant
(Neper/m)
Phase constant
Transmission Line Equation
First Order Coupled Equations!
WE WANT UNCOUPLED FORM!
Pay Attention to UNITS!
Wave Equations for Transmission Line
Impedance and Shunt Admittance of the line

7. Lossless Transmission Line
If
Then:
Non-dispersive line:
All frequency components have the same speed!
What is Zo?